In summary, yes plenty of time if you don't look around and burn up time and your incoming is not delayed.

There is a bus in front of Songshan that go to Taoyuan. Bus stop 6, bus number 1840, but it makes pitstops along the way, it's well over an hour of ride. No transfer or change, it's door to door, leave Songshan 3 times per hour. Bus stop person and driver do not speak English, so you need to make it simple "tao yuan ji chang?" to confirm it's the right bus and they will nod and you are good. You pay the bus stop person to get a ticket.

Your other option is to take MRT subway to Taipei Main (train) station, but it's brown train followed by transfer to blue train, exactly 35 min. You then transfer to the new MRT train for Taoyuan - make sure you board the Express train, other wise it stop at every station. The Express train is 45min, which arrives in the basement of the arrival, just take escalator up to departure.

Safest and quickest, is to take a taxi from Songshan to Taoyuan, then onto the MRT Express train.

You should check when with EVA when you arrive - there should be a bus provided by Evergreen, parent of EVA (not sure if still runs, but the 3 public options I listed above are all safe)